1 . 如图所示数阵,第
行共有
个数,第
行的第1个数为
,第2个数为
,第
个数为
.规定:
.
(2)从第1行起,每一行最后一个数依次构成数列
,设数列
的前
项和为
,是否存在正整数
,使得对任意正整数
,
恒成立?如存在,请求出
的最大值;如不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5726ebd95b22e5f7971028479790df77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623207595425920f16e76a7f8f268b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29a285201fd7e0ad70fa7431cb89a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0749c4129afc0c704155f522290b25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee754f9af67705c16c167733b5ef75db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5222268dda9dcb9b660f3cbedbb37757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ef9ec4340eabb42722042c65cc60d8.png)
(2)从第1行起,每一行最后一个数依次构成数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e8660fb54ba32b037b392b75316087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
2 . 已知不等式
的解集为集合A,集合
.
(1)若
,求
;
(2)若
,求实数
的取值范围;
(3)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7e48dd3bc72004e6549a51c3d98ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65397186779d9205c93b1ba96145dadd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
3 . 已知定圆
,动圆P过点
,且和圆
相切.
(1)求动圆圆心P的轨迹E的方程;
(2)设P是第一象限内轨迹E上的一点,
的延长线分别交轨迹E于点
.若
分别为
,
的内切圆的半径,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fdc28de4b46c7a176ba6858a856a918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
(1)求动圆圆心P的轨迹E的方程;
(2)设P是第一象限内轨迹E上的一点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d82387e48eafb286785a21a8d4150f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357e0872d9e98d662a780e7686de86ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8543261a8e351eb95cdfebb001a3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7733784336d1592cfe38e6a629140ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01d20fc53563351369c9bcb1360c410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fd3d19b0c8b544d52b897ca30990b4.png)
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名校
解题方法
4 . 已知全集
,集合
,
.
(1)若
,求实数
的取值范围;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/442be389c6471b36eff2652b75beb114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9607925e9edd5482fabdcb6d3a4d1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6001de7ff4d09f756e62c14537e2b654.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b05d2be27e8f53e4de3071846dffb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac59877d187318610e6db3f2a926ad73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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5 . 已知椭圆
的离心率为
,且过点
.过椭圆
上的点
作圆
的两条切线,其中一条切线与椭圆
相交于点
,与圆
相切于点
,两条切线与
轴分别交于
两点.
的方程;
(2)
是否为定值,若是,请求出
的值;若不是,请说明理由:
(3)若椭圆上点
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90627d25fa0d0e5345c834b96331e77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959e5ab675f526dfb54b05f8f82151b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2228629b80d4efbfd2a226a863274520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2228629b80d4efbfd2a226a863274520.png)
(3)若椭圆上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c81a4d934b8e4565969a8e7921111c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
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名校
6 . 已知集合
,其中实数
是常数.
(1)求集合A与集合
;
(2)若对任意的
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea3ac2f45b27e6f22bddfdc1ca0ef72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)求集合A与集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 如图,点
均在
轴的正半轴上,
,
,…,
分别是以
为边长的等边三角形,且顶点
均在函数
的图象上.
个等边三角形的边长
;
(2)设数列
的前
项和为
,求
.
(3)已知数列
的通项
,数列
中,
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce1e808127c5672eb1b47024e54c9cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb99c20237aca8ff2ba640c28fbc5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a619e2751f422ae187505e95339d02fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b80801bd92f36541707eea1229685e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699bdb06cc1a8e431fd96fdd06f6d2f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a6e162176d244084d154bc50b598eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d876a9e0ab9abc3880410cfde910eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ef48976a52cc4a2be7c46a98426c0a.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267c99ff3f6386113dbaa7b1e49612da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e1ee88beaddafb0d0a185c3a8e0dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a655f0f5afe3673c421af8a677b5154c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8427946085d576e0696e06cf4463c30f.png)
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8 . 某高中学校有室内、室外两个运动场.假设同学们可以任意选择其中一个运动场锻炼,也可选择不锻炼,一天最多锻炼一次,一次只能选择一个运动场.若同学们每次锻炼选择去室内、室外运动场的概率均为0.5,每次选择相互独立.设
同学三天内去运动场锻炼的次数为
,已知
的分布列如下:(其中
)
(1)记事件
表示
同学三天内去运动场锻炼
次
;事件
表示
同学在这三天内去室内运动场锻炼的次数大于去室外运动场锻炼的次数.当
时,试根据全概率公式求
的值;
(2)是否存在实数
,使得
?若存在,求
的值;若不存在,请说明理由;
(3)记
表示事件“室外运动场举办集体锻炼活动”,
表示事件“王同学去室外运动场锻炼”,
.已知
同学在室外运动场举办集体锻炼活动的情况下去室外运动场锻炼的概率,比不举办集体锻炼活动的情况下去室外运动场锻炼的概率大,试比较
与
的大小,并证明之.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e362ab25e6f8719efd1b515094b69561.png)
![]() | 0 | 1 | 2 | 3 |
![]() | ![]() | ![]() | ![]() | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eef5855dd54b607a61027e0b212cd61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108ab49f370919e730e3567070deee65.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667df0f959f5626681d6d9aecaf05be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efafab9402e42c2212489d7b9408c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697e2bfec979c21b2ba96569f82dba64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519abef903d663a9633f5ac89bc45fe0.png)
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名校
9 . 有甲乙两个骰子,甲骰子正常且均匀,乙骰子不正常且不均匀,经测试,投掷乙骰子得到6点朝上的概率为
,若投掷乙骰子共6次,设恰有3次得到6点朝上的概率为
,
是
的极大值点.
(1)求
;
(2)若
且等可能地选择甲乙其中的一个骰子,连续投掷3次,在得到都是6点朝上的结果的前提下,求这个骰子是乙骰子的概率;
(3)若
且每次都等可能地选择其中一个骰子,共投掷了10次,在得到都是6点朝上的结果的前提下,设这10次中有
次用了乙骰子的概率为
,试问当
取何值时
最大?并求
的最大值(精确到0.01).(参考数据
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098e663b79254b0a2e0e00f92bd14b8d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098e663b79254b0a2e0e00f92bd14b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcbd28fefa404513768b10747e2291a.png)
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23-24高二下·上海·期末
解题方法
10 . 已知椭圆
,抛物线
.若直线
与曲线
交于点
、
,直线
与曲线
分别交于点
、
.当
时,则称直线
是曲线
与
的“等弦线”.
(1)求椭圆
的离心率;
(2)直线
同时满足以下两个条件:①直线
经过原点②直线
是
与
的“等弦线”.请求出
的方程;
(3)已知点
,
,证明:过点
存在
与
的“等弦线”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8182955e08c6b0f37dff638dddf38a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd6bbdea60f11133f9004d242c81ca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd82bf82c3254c27b00f65b9a697e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d227daf0c0cf6822f3888e3f3de5f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bd62d197e1e52522c1c0347767eec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
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